Geometry Problem 1492: Right Triangle, Altitude, Incenters, Angle, Measurement

The figure shows a right triangle ABC with altitude BD. Points O, O₁, and O₂, are the incenters of triangles ABC,ABD, and BDC. If the measure of angle OO₂O₁ is 27 degrees, find the measure of angle O₁O₂D.

See solution below

Incircle, Incenter

Incircle is a circle within a triangle, that is tangent to each side. The incenter is the center of the triangle's incircle.